FracturedReservoirModeling

SS2014Dr.RainerMller

Whatisafracturedreservoir?Thebehavior,capabilityofstorageandmovementoffluidsandgasesinrocksisgenerallycontrolledbytheproportionofopenspaces(pores,interstices)intherockmatrix.Thisattributeofrocksisdescribedasporosity.Theporesmaybeinterconnectedorisolated.

absolute porosity Pt =(bulkvolume solidvolume)/bulkvolumex100effectiveporosityPe =interconnectedporevolume/bulkvolumex100

Aswell,thematrixpermeability thecapabilitytotransmitfluidsorgases iscontrolledbytheeffectiveporosity.

Primaryporosityisdevelopedduringsedimentation.Inclasticrocks,theprimaryporositycorrespondsatalargeextendtotheintersticesbetweengrains,andiscontrolledbythegrainsize,theroundnessandthepackageofthegrains.

TypesofPorosity

Secondaryporosityorinducedporosityistheresultofgeologicalprocessesactingafter theformationofrocks.Possiblecausesare: Fundamentaljointpatternbylossofwater), thedissolutionofsoluteprimarycomponents (pressuresolution,stylolites)or

dolomitization inlimestones and thetectonical formationoffractures.

Porositymaybedistinguishedintoeffective(open)andineffective(closed)porosity.

Vuggy porosityisaspecialtypeofsecondaryporosity,duetotheirregual dissolutionofof largercomponents,suchasfossilsincarbonaterocks.

Whatisafracturedreservoir?Fracturesmayincreasetheeffectiveporosityofrocksbyinterconnectingtheprimary(matrix)porosityand(inconsequence)thepermeability(fracturepermeability).So,theymaysupporttheflowofhydrocarbonsreservoirs,thus,theproductionrate.Insomehydrocarbondepositsfractureassemblagesaretheleadingfactorsofthedeposits.Thesedepositsarecalledfracturedreservoirs.

Therefore,theknowledgeoftypesoffractures,theirbehaviorandtheiroriginisofmajorimportancefortheexplorationandproductionofhydrocarbons.

Ontheotherhand,astheformationandopeningoffracturesdependonpressure,theclosureofopenfractureduringextractionofhydrocarbonscoulddowngradeflowrates.

TheUseofFracturesinPetroleumReservoirsFracturespresentbothproblemsandopportunitiesforexplorationandproductionfrompetroleumreservoirs.Manypetroleumreservoirsweregeneratedinhighlyfracturedrocks,wherefracturepropertiessuchasdensityandorientationarecrucialtoreservoireconomics.Thisaspectappliesespeciallytocarbonatereservoirs.Inmostcasesthefracturesareusuallyimportantofpermeabilityratherthanporosity.Matrixporositystoresthehydrocarbons,andfracturesprovidepermeablepathwaysfortheirtransport.Theobjectiveofhydrocarbonexplorationinfracturedreservoirsistofindareasofintensefracturing,orsweetspots.(CommitteeonFractureCharacterizationandFluidFlow1996)

Fracturedhydrocarbonreservoirsprovideover20%oftheworldoilreservesandproduction.Examplesoftheprolificfracturedpetroleumreservoirsare:

1) theAsmari limestonereservoirsinIran,2) thevugular carbonatereservoirsinMexicoand3) thegroupofchalkreservoirsoftheNorthSea.

Thesereservoirsproducemorethanfivemillionbarrelsofoilperday;theircommonfeatureisalonglifespan,whichcouldlastseveraldecades.

Thereisalargenumberofotherfracturedhydrocarbonsreservoirsofverydifferentfeaturesfromtheabovereservoirs. TheAustinchalkfield, theKeystone(Ellenberger)fieldinTexa,and theTempa Rossa fieldinItalyThosedepositshaveverylowporosities.

Ontheotherhand,theaveragematrixporosityoftheEkofisk chalkfieldintheNorthSeaisaround35%.

FracturesinPetroleumReservoirs:Examples

UnconventionalGasReservoirs

Inthelastyears,majoreffortshavebeentargetedonunconventionalgasreservoirs,suchasshalegasortightgasorcoalbedmethane.Thesedepositsarecharacterizedbyverylowpermeabilitiesandadsorptionofgasintotherockmatrix.Inthiscase,fracturesarenotonlyusedfortheproductionofgasbutalsoartificiallygeneratedbythetechniqueofhydraulicfracturing(orabbreviatedasfracking).

Tectonicfracturesarenotrandomlydistributedintheearthscrustbutrigidlycontrolledby

typesofrocks,theircomposition,rheologyandthickness, typesoffractures, locationanddepth, density, filling(aretheyopenornot)andtypeoffilling orientationsand the(originalandactual)stressfield.

Theyareconcentratedatdistinctzones(zonesofweakness,fracturezones).Theirorientation(strike,dip)isstrictlycontrolledbyorientationandtypeoftheactingstressfieldduringthetimeofformationofthefractures.

Whatshouldweknowaboutfractures?

Whatarewegoingtotalkabout?

Basicdefinitionsandtypesofthedifferentfractures

Measuringandreconstructionoffractures

Methodsofrepresentationoffractures(roses,stereographicprojection)

Factorscontrollingtheformationandpropagationoffractures

(Stressfields,Mohrcircle)

TypesofGeometricalElementsinGeology

Planes

Lineations

TypesofPlanesinGeology1)PrimaryPlanes

areplanes,whicharegeneratedduetotheprocessofformationoftherocks.Beddingplanes(stratificationplanes):

areresultofsomekindofinterruptionorchangeofthesedimentationprocess areoriginallyorientatedparalleltotheearthsurface(horizontal) showawiderangeofdifferenttypes,combinations(beddingtypes)andgeometries areaffectedbylatertectonicalinfluences(fractures,folds,pressuresolution) maybedistinguishedfromotherplanesbyobservationofchangesofmaterial

TypesofPlanesinGeology1)Beddingplanes:Examples

left:parallelbedding(flatbedding)ofsandstone siltstoneintercalations

right:irregularbeddingplanesofthickbeddedlimestones

TypesofPlanesinGeology1)Beddingplanes:Examples

left:ripplebeddinginsandstone

right:laminationinmudstones

TypesofPlanesinGeology2)Metamorphicfoliation,cleavage

Foliationissecondary,tectonicallycontrolledtypeofplanesinrocks,commonlydevelopedinfinegrainedshalesandleadingtorocks,whicharecalledschist.Foliationorschistosityorcleavageisareactionofrocks,whichwereexposedtoextremetectoniccompression.

Penetrativeaxialplanecleavageinfoldedschists Complexfoldingofmetamorphicfoliationinamphibolites

TypesofPlanesinGeology3)Fractures

Fracturesaresecondaryseparationplanesoftectonicorigininrocks,whichmaybesubdividedintothreetypes:

a) Joints

b) Fissures

c) Faults

TypesofPlanesinGeology3a)Joints

Jointsarecommonandfrequentfracturesinanytypesofrocks.

Jointsareseparationplanes,cracks,inrockswithoutanyvisible(oremeasurable)verticalorhorizontaldisplacement.

Inthesenseofviewoffracturemodelling,theyareofmayorimportance.Differenttypesanddifferentoriginsofjointsareknown.

Plumosestructures:areindicatorsforcrackpropagationonjoints

Differentintersectingsetsofjoints

TypesofPlanesinGeology3b)Fissures,tensiongashes

Fissuresarejointlikefractureswithameasurablehorizontaldisplacementnormaltotheorientationoftheplane.Itmeans,thatfissuresare(originally)openstructures,whichareofmayorimportanceforthemigrationandthetransportofliquidsandgas.Inmanycasesfissuresare(secondarily)filledwithmineralprecipitationslikegypsum,calciteorquartzorevenraremineralslikeores(veins).Tensiongashesare(normallysmallscaled)structuresasaresultoftensionalstress.

TypesofPlanesinGeology3c)Faults

Faultsareseparationplanesinrocksshowing(megascopically)visibleandmeasurabledisplacement.Thedisplacementmaybeobservedby:

Setofthreenormalfaultsdisplacingalimestonelayer(Alps,fromRamsay)

thedisplacementofmarkerbeds, by striations along the fault plane or by dragging of the nearby beds.

Strikeslipfaultinlimestones (LeinetalRift,Mller)

Typesoflineationsingeology:(primary)sedimentarylineations

Manynontectonical,primarytypesoflineations,especiallyinsedimentology,areknown,whichprovideuswithinformationabouttransportdirectionsandsourcesofsedimentarymaterial.

Flutecasts,striationmarks,groovecastsarethebestknownstructuresofthistype.However,eveninigneousrockslinearalignmentofneedleshapedmineralsservesasindicatorofflowdirectionsandinfluxmechanismsofmelts.

Flutecastsonadownsidedbeddingplaneofoverturnedgreywackesequences,Harz

Typesoflineationsingeology:FoldaxisFoldaxis(hingelines)aretheconnectinglinesoftheinflexionpointsofafold,atwhichtheconcavityofthelimbsreverses(eitheranticlineaxisorsynclineaxis).Foldaxisarethemostimportantgeometricalelementtodescribetheorientationandtypeoffolds.

Typesoflineationsingeology:Foldrelatedlineations

Fishmouthstructurebetweenboudins inmarbles;Matreishearzone,Austria.

Mullionstructureinaalternatingsequenceofgreywackes andslates,Eifel(RAMSAY)

Typesoflineationsingeology:Intersectionlines

Infoldedrocks,theintersectionlineationsbetweenfoldrelatedplanescorrespondtotheorientationofthefoldaxis.Intersectionsofplanesofthesameorder(suchasbeddingplanes)arecalledlineations.Intersectionsofplanesofdifferenttype(andorigin),forinstancebeddingplanes(s0)andcleavage(s1)arecalledlineations.

Pencileshapedpiecesofslates,formedbyaobtuseanglebetweenbeddingandcleavage(lineations).Thelongaxisofthepencilsrepresenttheorientationoffoldaxis.

Typesoflineationsingeology:Mineralstretching

Typesoflineationsingeology:Mineralgrowth

Newformingorrecrystallized needleshapedmetamorphicmineralsoraggregatesofmineralsundercontinuouscompressional stressconditionsaregrowingparalleltotheminorstressaxis.

Needles Platyshapedminerals

Typesoflineationsingeology:Striation

Vertical striations and crescentlike edges indicate, that the (upper) hanging-wall block was displaced vertically downwards, resulting in a normal fault.Jurassic limestones, French Jura, (diameter of the picture: 1m), Photo: Mller

Striationsarescratchmarksonfaultplanes,formedbythetectonicaldisplacementprocessofthetworigidblocksalongthefaultplane.Theyareofmajorimportance,astheydemonstrateustherelativeandabsolutedisplacementdirection.

Wheredoesstructuralinformationcomefrom?

a) superficialoutcrops:

Advantages: easilyaccessible,lowcostsexposedin3dimensionsatlargeextensionslargenumbersofdatamaybecollectedrelativetemporalandspatialrelationsofdifferentelementsandgenerationsmaybedistinguished

Problems: transferofsuperficialinformationtothedepth

b) Drillings:informationonfracturesmaybeobtaineddirectlyfromcores,fromvideorecordingsofthedrillholeorfromspeciallyprocessedlogsorcombinationsoflogs,producing3Dimages.

Advantages: informationmaybeobtaineddirectlyfromthelocationofinterest

Problems: highcost,verylimitedrageofinformationinspace,limitednumberofdataorientationandmeasurementofelementsisdifficult

Wheredoesstructuralinformationcomefrom?

b) Seismics:interpretationsofresultsofseismicexplorationin2Dand3D

Advantages: informationmaybeobtainedregionalscaleundgreatdepth

Problems: highcost,limiteddetaileddissolution,minorstructuresdifficulttoanalyse,orientationandmeasurementofelementsisdifficulttoanalyse,

Wheredoesstructuralinformationcomefrom?

Typesofstructuraldata,tobecollected

Spatialorientationofthefractures: eachkindofstructuralmodelingdependsbasicaly ontheorientationofthefracturepatterninastatisticalpointofview.Forrepresentationandanalysisofthedataspecialmethodsasrosediagramsandstereographicrepresentationareneeded.

Analysisoftype,relationsandoriginofthefractures: usingjoints:observationofgenetically,temporallyandspatiallyrelatedjoints(setsofjoints).usingfaults:observationofthetypeoffaults,kinematicsanddimensionofdisplacement.

Spatialrelation,densityofthefractures: veryimportantfortheinterpretationoftheroleofaspecialsetofjointsaspathwayforthemigrationoffluids.Thenumberofjointsofaspecialorientationhastobecountedandbereferredtoanormalizeddistance.

Openingandfillingoffissures

MeasuringtheOrientationofPlanes

StrikeN

Dip direction

horizontal plane

Dip angle

Strikedescribestheorientationofan(imaginary)horizontallineonaninclinedplane(tothenorthdirection).Strikeisspecifiedbetween0and180.

Dipdirectionistheorientationofthelineofsteepestpossibledipangleonaninclinedplane(tothenorthdirection),normaltostrike.

Dipangleistheanglebetweentheplaneinquestionandan(imaginary)horizontalplaneindipdirection.Dipangleisspecifiedbetween0and90.

GeologicalCompass

Brunton compass

GeologicalCompass

GermanMiners Compass

GeologicalCompass

GermanClar Compass

Notationof structural data:planes070/40SE 160/40 N070E,40SE125/10NE

010/80W

170/05W

30/10NW

160/80W110/50NE

140/10SW

050/15NW

000/40W090/50N

180/90

035/10

280/80

260/05

300/10

250/8020/50

230/10

320/15

270/40

000/50

090/90

N055E,10NE

N010E,80W

N010W,05SW

N030E,10NW

N020W,80W

N070W,50NE

N050W,10SW

N050E,15NW

N000,40W

N090E,50N

N000,90

MeasuringtheOrientationofLineations

N

Trenddescribestheorientationofan(imaginary)horizontalprojectionofthelineationtothenorthdirection).Trendisspecifiedbetween0and180.

Plungedirectionisthedirectionoftheinclinationofthelineation(tothenorthdirection),paralleltothetrend.

Plunge(angle)istheanglebetweenthelineationinquestionandthe(imaginary)projectionofthelineationtoanhorizontalplaneinplungedirection.Plungeisspecifiedbetween0and90.

horizontal plane

Plunge (angle)

Notationofstructuraldata:lineations

130/40SE 130/40 S050E,40015/80NE

15/10NE

140/42NW

050/30SW

100/54NW170/80N

010/20N

030/13SW

014/50S140/00

065/14SW

015/80

015/10

320/42

230/30

280/54350/80

010/20

240/13

194/50

140/00

245/14

N015E,80

N015E,10

N040W,42

50,S030W

80,N54W

10,N80N

10,N020E

60,S13SW

S014W,50

N040W,00

S65W,14

ClassificationofFaults

ClassificationofFaults

Normalfaults

Reversefaults

Strikeslipfaults:G:sinistralI:dextral

CombinationsofNormalFaults

TypesofReverseFaults

Reversefault:dip>45 (~65)

Thrustfault:dip

Exercise:Determinationoftypeanddisplacementoffaults

Quantitativedeterminationofdisplacementratesoffaults(1)

Todeterminethedisplacementrateof(verticallydisplaced)faultsingeologicalmaps,twotriangularrelationsmaybeused.Thefirstgeometricalconstructionisexecutedalongasectionverticallytothefaultplanewiththecomponents:

s =(apparent)horizontalwidthofdisplacement(=horizontalcomponentofw)(heave),t =verticalwidthofdisplacement(=verticalcomponentofw)(throw),w =(real)widthofdisplacement(slip)

Quantitativedeterminationofdisplacementratesoffaults(2)

Usingthethrowt,theformertrianglemaybecombinedwithasecondtrianglearrangedverticallytothebeddingofdisplacedrocks,whichusesanapparenthorizontalrateofdisplacementsh (strikeseparation).Thestrikeseparationsh canbemeasuredalongalineofstrikebetweenthesameplaneofadisplacedlayer.

tan(bedding)=t/sh;t=sh *tan(bedding)

sin(fault)=t/w;t=w*sin(fault);w=t/sin(fault)

cos(fault)=s/w;s=w*cos(fault);w=s/cos (fault)

tan(fault)=t/s;t=s*tan(fault);s=t/tan(fault)

Quantitativedeterminationofdisplacementratesoffaults(3)usingtrigonometricfunctions

Exercise:QuantitativedeterminationofdisplacementratesoffaultsCalculatedisplacementratesandcompletethesketchesofmaps,assumingpureverticaldisplacement

Scale1:10000

Joints

Definitions: Jointtrace:intersectionlinebetweenajointplaneandanyotherplane. Jointset:isasetof(moreorless)parallelorientatedandgeneticallyrelatedjoints. Jointzone:section,inwhichajointsetofspecificorientationareconcentrated

(comparedtoitssurroundings). Jointsystem:theentiretyofthejointsetsofdifferentorientationsinaregion,

whichmaybeconsideredasgeneticallyrelatedtothesamestressconditions.Thosejointsetsmaybesymmetricallyorientated,forexampleorthogonallyorientatedjointsorconjugatesetsofjoints.

Jointpattern:theentiretyofalljointsofareregion,whichmaybecomprisedofseveraljointsystemswithgeneticallyandtemporarydifferentorigin.

Jointsarefractureswithoutvisibleormeasurabledisplacementinrocks

SystematicjointsJoints,whicharegeometricallyregular(parallel,orthogonal)(jointsystems)intheirarrangementarecalledsystematicjoints.

Lessregularjointsarecallednonsystematicjoints.Theyarenormallyofaminorscaleandofirregular,randomorientations.Nonsystematicjointsmaybeoriginatedbylocalvariationsofrheologicalparameters.Theycanhardlybepredicted.

NonsystematicJoints

Joints

Manyjointsystemsexhibitregionallyconsistentpatternsoforientations,whichareobservedtopersisteventhroughoutthestratigraphicsection.

Insedimentaryrocksasystematicperpendicularorientationofjointstothebeddingplanesiscommonlyobserved,frequentlyshowinganorthogonalarrangement oftwosetsofjoints.Thissocalledfundamentaljointsystemseemstobegeneratedalreadyduringearlydiagenesis.Sometimes,theorientationofthesystemcorrespondstotheaxisofthebasin.

Therefore,thearrangementofjointsinsedimentsfrequentlyshowsrelationstotheshapeofthesedimentarybasin.

Mostobservationsonjointsimply,thattheyhavebeenformedundertensilestressconditions.Nevertheless,compressiveregimenisthecommonstateofstressintheearthscrust(load!),therefore,effectivestress,controlledbyfluidpressure,playsanimportantroleinjointformation.

Joints

Thespacingofjointsinsedimentarylayersiscontrolledbytheelasticbehaviorandthicknessofthebeds.Therefore,spacingdiffersinmanysequencesfromlayertolayer.TheelasticbehaviorofrocksisdescribedbytheYoungmodulus,whichisameasureoftheirstiffnessanddescribestherelationbetweentensilestressandstrain.

Fissures,tensiongashes

Fissuresareopenstructures,combinedwithextensionalstressconditions.Theyarearrangedintypicalorientationstotheappliedstressfieldandthecorrespondingmajorstructures(faults).

Mineralfibers(gypsum,calcite,quartz)infissurescrystallizeparalleltotheminorstressaxis3Photo:RODRIGUES etal.(2009):J.Geol.Soc.;166:.695709

Representationofstructuraldata

Structural datasets normally involve the following features: they represent the 3-dimensional orientation of planes or lineations, they include normally a large number (several tens or hundreds) of samples, they include different types of structural elements (bedding, faults, joints),

whose geometrical relations are known and must be verified.

Please note: Directional data, expressed by strike and dip, can not be treated statistically as two independent values, but are 3-D vectorial data ! For statistical analysis of gravity centers of orientation and their variation, special complex methods of vector analysis are required.

These large and complex directional datasets must be interpreted and represented in a 3-dimensional system.Two methods are in use: Rose diagrams and stereographic projection (Schmidt Net)

RosediagramsInrosediagrams(only)thetrendofstructuralelementsisusedfortheconstructionofadirectionalhistogramshowingthefrequencyofdataofcertaindirectionalclasses,representedina360 or180 circle(rose).Itisfrequentlyusedforsteeplydippingjointsetsorotherdatainwhichthedipangleisnotimportant.

Rosediagrams:ExampleData: Orientations of 64 joints

10/48 E 94/80 S 63/74 NW 154/68 SW 14/68 ESE 07/56 E 149/70SW 59/80NW12/68 E 109/88 N 163/67 NE 17/81 ESE 90/80 S 12/66 E 94/73 S 13/83 E01/81 W 06/78 E 62/85 NW 149/70SW 16/77 E 04/68 E 150/75SW 80/59N06/60E 91/81 S 64/75/NW 155/69/SW 15/68 ESE 08/77W 148/76SW 60/60 SE12/49 E 93/80 S 69/74 NW 151/68 SW 13/68 ESE 06/56 E 147/70SW 61/80NW12/83 E 111/88 N 161/67 NE 20/81 ESE 89/80 S 15/66 E 91/73 S 09/83 E03/84 W 10/78 E 65/85 NW 151/70SW 19/77 E 02/68 E 152/75SW 79/59N07/66E 94/81 S 59/75/NW 148/69/SW 13/68 ESE 11/77W 146/76SW 66/66 SE

Rosediagrams:Differenttypes

Rosediagrams:Resultsoftheexample

max = 26.98%

0

90

180

270

90

0

bung Kluftrosen.pln Datasets: 63

Interval: 10

Interval: 10

max = 33.33%

Rosediagrams:Resultsoftheexample

Analysis of the example data using TectonicsFP

Applicationofjointdiagrams

Stereographicprojection(SchmidtNet)

Theintersectionoftheelementwiththespheressurfaceleavesatraceinformofacirclesegment(plane)orapoint(line).

Thesecondmethodofrepresentationofdirectionaldataismuchmoremeaningful,howevermoredifficulttounderstand,touseandtointerpret.

Inthiscase,planesorlines,areconsideredtobearrangedwithinina(imaginary)sphere,passingthroughthecenterofthesphere.

Thepositionofthetraceorthepointoneithertheupperorthelowerhemisphereisprojectedtoaplanepassingthroughthecenterofthesphere.

Polar(normal)or azimuthal Projektion

The projection may be polar (a) or azimuthal (b).

Polar projection is applied as the so called polar net.Longitudes are represented as straight lines; latitudes as circles with differing radii.

For the Schmidt net azimuthal projection is used.Latitudes and longitudes are +/- curvilinear segments of a circle; equator and N-S-axis are represented as straight lines.

TypesofProjection

Spherical surfaces may be projected as: equal angle (Wulf net, Mercator), equal length or equal area (Schmidt net).

Equal angle projection is used for the correct representation of angular relations, for example the angles between crystal planes in crystallography.

The Schmidt net projection is of equal area type. Equal area relations are needed for a statistical analysis of the population density of representing point on the surface of a sphere.Equal angle relations are represented without distortion along great circles.

Stereographicprojection(SchmidtNet)

Model Projection

SchmidtNettop:polar(normal)projectionbottom:azimuthalprojection equalareaprojection

Net

SchmidtNetN

S

EW

NW NE

SESW

Equator

greatcircles(meridians)

smallcircles

1020

3040

Transparency Layer

PreparationoftheNet:

Fixapinfromthebacksidethroughthecenterofthenet

Fixatransparencylayer

Orientatelayersparallel

Markcenter(cross)

Markoutercircle

MarkNPosition

N

Representationofaplane(70/20NW)asgreatcircle

Preparethetransparencylayer

Rotatethelayerwith70 counterclockwise

Count20 onequatorfromoutsidetocenter

Markthecorrespondinggreatcircle

Rotatethelayerbacktoorigin

N

Representation of lineations Example: (70/20NE)

Preparethetransparencylayer

Rotatethelayerwith70 counterclockwise

Count20 alongNScenterlinefromNtocentertocenter

Markthecorrespondingpoint

Rotatethelayerbacktoorigin

N

Inthepetroleumprospectionfield1highflowrateshavebeendetectedintheverticaldrillhole DH1atadepthof1000m,obviouslycontrolledbytheintersectionoftwonormalfaultzones.Theirorientationsare:Fault1:125/35Fault2:156/551)Locatethepossiblecorridor,inwhichthisintersectionzonecouldcrosstheprospectoffield2andselectapossibledrillinglocation.2)Atwhichdepththefavorableflowratesaretobeexpected?

Exercise:Determinationofahighpermeabilitypathwaybytwointersectingfaults

Point counting: Statistical evaluation of structural data

One of the most typical applications of stereographical projection of structural data is their statistical evaluation. The scope of these procedures is the determination of the center(s) of gravity of a cloud of poles.The mathematical calculation of those parameters is complex. Orientational data in a 3-D space are vectors; their evaluation requires methods of vector analysis.Actually, some of those operations can be performed using special tectonic programs.A manual analysis is quite simple but time consuming.It is performed using a so called counting net (see next slides).

AnalysisofSchmidtnetdata

AnalysisofSchmidtnetdata

4Klassierung: 1 Punkt2 - 3 Punkte4 - 5 Punkte5-10 Punkte

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AnalysisofSchmidtnetdata

bung Kluftrosen.plnDatasets: 63

Max. value: 15.6%at : 101 / 69

Contours at:1.00 3.00 6.00 9.00 12.0

AnalysisofSchmidtnetdata:ExampleTectonicsFP

RepresentationofFaultsusingStereographicProjection.

.usingtheANGELIER method Example:reversefaultplane:200/80striation:270/60

StressandtheDeformationofRocks

Inacoordinatesystem,thestateofstressofasinglepointinasolidcanbeexpressedbythreeprinciplestressaxis,whichareorientatednormaltoeachother:

1 =inthedirectionofthemajorstress,2 =inthedirectionoftheintermediatestress,3 =inthedirectionoftheminorstress,

Stress isameasureoftheintensityandorientationoftheforcesperunitareaonadeformablebodyonwhichinternalforcesact.Deformationorstrainisthereactionofrockstostressandisdescribedbytherelationbetweenaninitialandfinalplacementofasolidexposedtostress.

StateofStressonaPlane

Thestateofstressonasinglepointonaplanewithinthesolidcanbedescribedby anormalstresscomponentn and two(perpendicular)shearstresscomponents1 and2

Onplanesperpendiculartooneofthethreeprinciplestressaxis,theshearstresscomponentsarezero.

Themaximumshearstressactsonaplane,thatbisectstheanglebetweenmaximumandminimumprinciplestress:

max =(1 3);

Thecorrespondingmaximumnormalstressequalsto:

n max =(1+3);

ANDERSONS TheoremofFaulting.

states,thatonahorizontalearthssurface,thereisnoshearstress,whichcouldcausemassdisplacement.Asaconsequence,oneoftheprincipalstressaxesmustbearrangednormaltotheearthssurface,thetwootheraxeshavetobeparalleltothesurface.Thisconceptleadstothreeprinciplestateofstresssituationsintheearthcrust:

1vertical:dilatation,normalfaults

3vertical:compression,reverse,thrustfaults

2vertical:compression,strikeslipfaults

Case1:

Case2:

Case3:

Stress:DefinitionsandUnits

Thestresstensormaybedecomposedintotwocomponents:MeanStress..

isthemeanvalueofthestressstate:m =(1+2 + 3)/3;

andrepresentstheisotropicpartofthestress

DeviatoricStress.isthedifferencebetweenaprinciplestressandthemeanstress:

i=i m;whichisresponsibleforalmostallcompressivedeformationalfeatures.

TheunitforstressisPa(Pascal)=N/mCompressivestressesareconsideredtobepositive!

1bar=105 Pa10bar=1MPa (megaPascal)=106 Pa

Pressureat5kmoceandepth:500bar=50MPa100MPa =1Kb(Kilobar)=1000bar

Pressureat30kmdepthofthecrust:approx.10kbar=1Gpa =109 Pa1atm (atmosphere)=1,0133x105 Pa

1kg/cm2 =0,9807bar

Lithostaticpressure..(orLoad)actsnormaltotheearthssurfaceandiscontrolledbytheloadoftherockpile,whichisdepth(inm)bydensity(atanaverageof2,5g/cm)bygravitationalconstantof9,82msec.LithostaticpressureisalsoexpressedasverticalstressvExample:Rockpileof5000m,density:2,5g/cm500000cmx2,5g/cm=1250000g/cm=1250kg/cm1250kg/cmx0,9807=1225bar=1,225Kb1,225KB=122,5MPa

HydrostaticPressure..(confining,geostatic,fluidpressure)isthehydrostaticpressureofawatercolumninaspecificdepthduetotheforceofgravity:pfluid =depth[m]x0,1[g/cm](1000mx0,1=100bar=10MPa)Hydrostaticpressurehasthesamemagnitudeinthreedirections(confining).Internalporefluidpressurereducestheeffectivestrengthactingonthesolid.

EffectiveStress.isthedifferencebetweenmeanstressandfluidpressure:

3)3(

3321

*3

*2

*1* fluid

m

P

Stress:DefinitionsandUnits

TheMohrDiagramTheMohrdiagramisaveryimportanttoolforrepresenting,analyzingand,aboveall,understandingthestateofstress,actingonaplaneofanyorientationinastressedsolidmaterial(givenbytheprincipalstressaxes1,2,3).WewillconsiderMohrdiagramoperationsintwodimensionsonly.

Example:Aplaneinahomogeneouslystressedcube.Itsnormalincludesanangle (=shearangletheta)with1.

Thestateofstressactingonthegivensurface,definedbytheshearangle,canbydividedintotwocomponents:Thenormalstressn isactingnormaltotheplaneTheshearstress isactingparalleltotheplane,resultinginasheardisplacementalongtheplane

1 n A

A= ( cos+ sin)cos

3 n B

B = ( sin+ cos)sin

2321 sincos n

cossin)( 31

;2cos)2

()2

( 3131 n

;2sin)2

( 31

Trigonometricrelationsdeductedfromthediagram

solved for n:

solved for :

converted into:

PlottingtheMohrDiagramTheMohrdiagramrepresentsthestateofstressofamaterialusingn asxaxisand asyaxis.Thestressonasinglepointonaplaneplotsasapoint(n ,).Compressivestressplotsontheright,tensilestressontheleftsideofthediagram.Thestatesofstressofallpossibleplanesofagivenstressfieldarearrangedonacirclewithacenterofthemeanstress andaradiusofthedeviatoricstress.1 and3 plotonthecircleintersectionwiththexaxis.Theshearangle(2)isrepresentedbytheangleofalinebetweenthecenterandtherepresentingpointofaplane.Planesperpendicularto1 and3 (with=90)havenoshearstress.Maximumshearstressoccursat=45.Thelargerthedifferencebetween1 and3 (deviatoricstress)thelargeristheshearstressonagivenplane.

TheMohrDiagram:Exercises

1) Theprinciplestresses1 and3 aregivenwith80Mpaand45Mparespectively.1 isorientatedhorizontallyinEWdirection,3 vertically.Whatisthestateofstress(n, )onafractureplanestrikingNSanddippingwith30 totheE?

Solution:=60,2=120max=17,5Mpaat =45nmax =62,5MPan =53,75MPa =15,15MPa

2) Thestateofstressismeasuredin2slotsofamine.Thefirstdips32Eandhasanormalcompressivestressn of57Mpaandashearstressof12Mpadowndip.Theseconddips84Eandhasanormalcompressivestressnof40Mpaandashearstressof3Mpa.Whatisthestateofprinciplestressesandtheirorientationinthisregion?

Solution: Constructthetworepresentingstresspoints,Bisectorlineinterferingthexaxisresultsinthecenter ofthecircle:1=66,5MPa,3=40MPa

TheMohrEnvelope:GatheringExperimentalData

Triaxial testingapparatus(fromSUPPE 1985:152)

Piston

Resultofatriaxial testofacylindricalshalesample(Inst.ofGeology,TUClausthal)

TheMohrEnvelope:ResultofanExperiment

Mohrdiagramofthefractureexperimentataconfiningpressureof50Mpa.Thediagramrepresentsthreedifferentstatesofdeformation.Therockprobefailedataloada of750(800load 50confiningpressure)Mpa (fromSUPPE 1985:152).

longitudinalstrain:

Stressstraindiagramofthetests(fromSUPPE 1985:152).Thenearlylineartrendisaresultoftheelasticbehaviorofthesample.

0

0 )(l

lll

common confining pressure c

TheMohrEnvelope

Mohrdiagramfordiabase sampleswithincreasingconfiningpressuresatroomtemperature.Eachcirclerepresentsthestateofstressatfailureatadifferentmeanstress.Therockstrengthincreaseswithmeanstress,dependingondifferentconfiningpressures.Thelocusofstressstates,thatboundsthefieldsofstableandunstablestresses,iscalledtheMohrenvelope(fromSUPPE 1985:153)

TheMohrEnvelope

ThreefieldsoffracturedevelopmentarerepresentedintheMohrenvelope. Thetensilefieldisrepresentedbyafixedtensilestrength T0.Onlyonedirectionofpossible

fractures,perpendiculartothedirectionofmaximumtensilestress,exist.Typicalvaluesoftensilestrengthare5to20Mpa.

TheMohrEnvelope

ThetransitionaltensilefieldislocatedbetweenT0 and1 >|5T0|andischaracterizedbyarapidnonlinearincreaseinmeanstrengthwithincreasingconfiningpressure.Mohrcirclesaretangenttotheenvelopeattwopoint;twoconjugateddirectionsoffracturesmayexist.Mostjointsareformedinthetensiledomain.

TheMohrEnvelope

TheCoulombfracturebehaviorrepresentsthelinearincreaseofshearstrengthcorrespondingtoincreasingconfiningpressure,characterizedbyaslopeoftan.

Theangleiscalledangleofinternalfriction. Itstangentiscalledcoefficientofinternalfriction,whichisamatterconstant. Athighconfiningpressureandincreasingtemperatures,strengthincreaseonlyslowlyat

ductilebehavior.

2)Ina6000mdeepdrillhole,thefollowingparametershavebeendetermined: Averagedensityoftherocks:2,7g/cm Densityoffluids:1,1g/cm Directionofh (usingbreakouts):150/00 h =0,5v H =0,8v Jointset1:330/60 Jointset2:60/60

Problems:a) Calculatetheprinciplestressesb) ConstructtheMohrdiagramrepresentingthestateofstressatthebottomofthedrillhole.c) Determinemeanstressanddifferentialstressd) Determinemeanstressandeffectivestresse) Drawasketchofthestateofstress,itsorientationandthesituationofthejointinthe

boreholef) Bytriaxialtestingexperiments,theMohrenvelopeoftherocksintheboreholehavebeen

determined.Willthejointsfailornotbythegivenparameters.g) Ifthejointwillnotfail,howcouldwetriggerthefracturegeneration?

TheMohrEnvelope:Exercise

Solution:

v =1 =159MPaH=0,8V =2 =127MPah =0,5V =3 =79,5MPaCenter=(1+ 3)/2=119,25MPapfluid =66MPa =38,06MPamax=40,5MPaMeanstress:121,8MPaEffectiveStress:55,8MPa

Onthebaseofexperimentaldataofthestateofstressandstraininrocksestimationstothefollowingproblemsmaybefound:

Themagnitudesofn and atthemomentoffailureoftherocksarerelatedtoeachother.TherelationisdescribedbyBYERLEEs law:Withincreasingnormalstressincreasescriticalshearstress:

crit =0,6 n to0,85 n inregionsofmoderatestress.

Thereare3possibilitiesintheearthscrust:1. 1 =2 =3 : thereisnoshearstressT2. 1 >2 >3: therearetwoplanesofmaximumshearstress

intersectingparallelto2 .Shearstressesachievetheirmaximumsymmetricallyto1 and3 withashearangleof45,resultingin(potentially)conjugatedfractures.

3. 1 =2 or2 =3: resultsinaninfinitenumberofplanesofmaximumshearstress

TheMohrDiagram:Consequences

Determinationofdifferentialstresses(1 3) DeterminationoftensilestrengthT0 ofrocks Determinationoftheangleofinternalfriction,whichiscontrolledbythegradientofthe

Mohrenvelope(mostly30) Determinationofthecoefficientofinternalfriction =tan(mostly0,55 0,85,inclays0,3

0,4) Estimationoftheinfluenceoffluidpressurepfluid anditsrelationtolithostaticpressurev,

whichismoreorless0,4inrespecttothedensitiesof1,0g/cmofwaterand2,7g/cmofrocksinopensystemsintheuppercrust.

Estimationaboutthepossiblestrainregimeandbehaviorofrocks(tensile,compressive,ductile)

Estimationaboutpossibleorientationsoffracturesinrocksaccordingtoanexistingorpreexistingstateofstress

Reconstructionofapreexistingorientationofstateofstressandthepositionofstressaxisusingaexistingfracturesystem

Simulationofconditions,underwhichtheformationoffracturescouldbesupported(hydrofracking)orimpeded,i.e.bycontrollingfluidpressure.

TheMohrDiagramWhatkindofinformationcanbederivedfromit?

TheOriginofJoints(fromSUPPE 1985)IntheMohrdiagramtheprincipledomainofjointgeneratingconditionsisthetensileortransitionaltensileregimen.Tensilefracturesformperpendiculartothedirectionofthemaximumtensilestress(between5and20Mpa).Transitionaltensilebehaviorisexhibitedabovetheleasttensilestrength.

Theequationforjointformationis: 0*3

*1 24)( T

0*3

*1 4)( T

0*1 3T

Forjointformation,themaximumdeviatoricstressequals:

whichisthelimitofthemaximumdeviatoricstressforatensileeffectivenormalstresstangentbytheshapeoftheMohrenvelope.

Fortruetensilejoints,themaximumeffectivestressislimitedto3timesthetensilestrength

Problem:Verticalstressisduetothegravitationalloadcompressive.Therefore,therequirementsfordeepformationofjointsare:

smalldeviatoricstressesand highfluidpressurerations

TheDepthofJointFormation(fromSUPPE 1985)

)1(3 0

gT

z

Usingtheaboveequationandtheequationforlithostaticpressure,maximumdepthofformationofjointcanbecalculatedas:

Forrockswithnormaltensilestrengthbetween2to10MPa,theformationofjointsislimitedto1or2kmofdepth,assuminglowfluidpressures(lowsalinities).

with: =meanrockdensityg=gravitationalconstant=fluidpressureratio

TheSpacingofJoints(from SUPPE 1985)Jointsperpendiculartobeddingisanimportantstructuralfeatureinsediments.Jointspacingiscontrolledby: rocktype:jointsaremuchmorecloselyspacedincoalthaninsandstones thicknessofthebeds:jointsaremorenumerousinthinbedsthanininterlayeredthickbeds

ofthesamerocktype. somejointsmaybelimitedtosinglebeds,otherspassthroughmanybeds.Considerapileofsedimentaryrocks,eachwiththicknessesd1,d2dn.andeachwithdifferentelasticconstantsE1,E2 En.anddifferenttensilestrengthT1,T2Tn,whereEistheYoungsmodule:

1 1 2 2 n nE E .......E

l

E

Thebedshaveundergonecompactionandareinthesamestateofstress.Thehorizontalstressandstraininalayeristhen:

Ifthesebedsareuniformlystretchedbyastrainx ,thenewhorizontalstress,generatedineachofthenlayerswillbedifferent: 1 1 1 xE

2 2 2 xE Asaconsequence,uniformstrainwillgeneratebedparallelnormalstress,whichwillbedifferentineachlayerofcontrastingelasticproperties.

and soon.

TheSpacingofJoints(fromSUPPE 1985)

Inthefieldweobserve,thatthespacingofjointscorrespondstothelayerthickness.ThesocalledGRIFFITH theory,states,thatthestressreleasearoundanewformedjointaffectsonlyaradiusofaboutonecracklength.Inconsequence,stressreleaseaffectsonlyashortdistancearoundthenewformedcrack,therestofthebedwillremaininanearfailuretensilestresscondition.Smallincreasesofstrainwillformnewjoints,sothatalayerwillbejointedin(moreorless)uniformdistancesequaltoitsthickness.Furthermore,stressreleaseinonedirectionmayinfluencethemagnitudesof 2 and3.Asaconsequence,theorientationofthenewformedjointschangeorthogonally.